NuMe – Numerical Methods for Internal Aerodynamics
This is a course on numerical methods for internal aerodynamics taught at Ruhr University Bochum. It covers derivations for fuluid models and their application using classical methods in Finite Difference, Finite Volumes and Time Integration methods. The course emphasizes both theoretical understanding and practical implementation of these numerical techniques.
This course was taught once in English during the summer semester of 2023 at Ruhr University Bochum.
Recommended previous knowledge:
- Calculus: integration, partial derivatives, Taylor Series, and coordinate systems
- Linear Algebra: solving linear systems
- Mechanics: momentum and force
- Thermodynamics: heat and energy
- Fluid mechanics: compressibility, laminar and turbulent flows, Navier-Stokes Equations
- Programming background: Python, matlab, etc.
Learning outcome, core skills
Completing the course successsfully, the student understands the principles of computer simulations for dynamic systems from the numerical point of view. This allows the student to analyze, derive, and implement a simulation of a flow model in a number of methods.
- The student understands the principles of discretization for conservation laws, in particular, equations of flow, and is able to identify the method/approach used in the simulation.
- The student analyzes and implements a workflow for a simulation using a numerical method/approach, with the ability to judge the accuracy and stability of their implementation.
- The student recognizes the difficulties and appropriate setups for internal flows.
Contents
- Review of important models in fluid mechanichs and thermodynamics: mass, heat, and momentum
- Review of important concepts in partial differencial equations: equation types and conservation laws
- Finite-difference method:
- Order of approximation
- Boundary conditions
- Solving the linear system
- Finite-volumes method:
- Volume average
- Interface interpolation
- Flux limiters
- Time discretization schemes:
- Order of approximation
- Implicit and explicit schemes
- Multi-step and multi-stage schemes
- Courant-Friedrichs-Lewy stability condition
- (Optional) Advanced topics:
- Multi-grid method
- Finite-element method
- Optimization based simulation: physics-informed neural network